The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm²) of the remaining solid?

In ∆ABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC= 18 cm, then the length of BD is:

The sum of the present ages of a father and son is 52 years. Four years hence, the son's age will be $${1\over 4}$$that of the father. What will be the ratio of the ages of the son and father, 10 years from now?

A can do a piece of work in 15 days. B is 25% more efficient than A, and C is 40% more efficient than B. A and C work together for 3 days and then C leaves. A and B together will complete the work in:

A and B are solutions of acid and water. The ratio of water and acid in A and B are 4 : 5 and 1 : 2, respectively. If x literes of A is mixed with y litres of B, then the ratio of water and acid in the mixture becomes 8 : 13. What is x : y ?

In ∆ABC, ∠A=90⁰ , AD is the bisector of ∠A meeting BC at D, and DE ⊥ AC at E. if AB = 10 cm and AC = 15 cm, then the length of DE, in cm, is:

if $${{5x-7}\over 3}+2={{4x-3}\over 4}+4x$$, then the value of (8x+5) is

The product of 1.7 ´ 10⁴ and 12.5 ´ 10^–6 is expressed in the standard form as k ´ 10ⁿ . The value of (2k + n) is